Using ifft2 to transform wavenumber-frequency to space-time

I have matrix of data in frequency-wavenumber domain and I want to transform this data into space-time. I use ifft2 to transform the data. I want to know what does the wavenumber tranform into as from the sampling frequency we get the time axis, hence what do we get from the wavenumber sampling and how to interpret this in the space domain

Answer 1

[David Goodmanson]

Chirag,

It's pretty clear in the time domain. With array spacings delt and delf in the time and frequency domain respectively, the golden rule for an N-point fft is

delf*delt = 1/N

Often this is accomplished using a sampling frequency Fs, with delt = 1/Fs and delf = Fs/N. But the golfen rule is more context-free than that.

For the an array in the variable w = 2*pi*f, the rule is

delw*delt = 2*pi/N

For space-wave# the situation is less clear cut. The most common use of k as "the wavenumber" is with the function exp(i*k*x), making k the equivalent of w as shown below. Unfortunately there is not a generally accepted symbol to be the equivalent of f. Spectroscopists use inverse centimeters, but that is a unit-dependent definition. I will just use a made-up g here in the following little table.

time-freq         exp(2*pi*i*f*t)      exp(i*w*t)      w = 2*pi*f       f = 1/period
space-wave#       exp(2*pi*i*g*x)      exp(i*k*x)      k = 2*pi*g       g = 1/wavelength

In space-wave# the golden rule is

delg*delx = 1/N
delk*delx = 2*pi/N

Both k and “g” are called wave number, so you will need to know which you have.